Bobs go broody as infrequently as most other domestic quail. Inbreeding coefficient will vary depending on the stock you have and what's been done with it by the previous breeder. Bobs have been kept domestically in the US for more than 125 years, plenty of time to inbreed the heck out of them.
Agreed... I dont feel the Inbreeding has much to do with it..... Bobs and other new world quail have been domesticated literally thousands of years less than old world quail... I feel this is why the new worlds remember their wild ancestors alot better than coturnix. Makes them less likely to tame and become comfortable be'n held as well. I also feel this is why, thou not common, bobs are more likely to go broody than cots, if given a natural like enclosure...... Odds are still against one successfully brooding and hatching in a captive setting. But the instinct to do so is still much stronger. Coturnix are much like pineapples, the reproduction instinct has been all but lost.
I do know of several breeders than have bobs do it every year.... almost exclusively these are raised in very large, ground pens with lots of cover...